Results 1 to 10 of about 234 (44)
Base sizes of primitive groups of diagonal type
Forum of Mathematics, Sigma, 2023 Let G be a permutation group on a finite set $\Omega $ . The base size of G is the minimal size of a subset of $\Omega $ with trivial pointwise stabiliser in G. In this paper, we extend earlier work of Fawcett by determining the precise base
Hong Yi Huang
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Symmetric graphs of valency seven and their basic normal quotient graphs
Open Mathematics, 2021 We characterize seven valent symmetric graphs of order 2pqn2p{q}^{n} with ...
Pan Jiangmin, Huang Junjie, Wang Chao
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A New Look at the Burnside–Schur Theorem [PDF]
, 2003 The famous Burnside–Schur theorem states that every primitive finite permutation group containing a regular cyclic subgroup is either 2‐transitive or isomorphic to a subgroup of a 1‐dimensional affine group of prime degree.
S. Evdokimov, I. Ponomarenko
semanticscholar +1 more source
The edge-regular complete maps
Open Mathematics, 2020 A map is called edge-regular if it is edge-transitive but not arc-transitive. In this paper, we show that a complete graph Kn{K}_{n} has an orientable edge-regular embedding if and only if n=pd>3n={p}^{d}\gt 3 with p an odd prime such that pd≡3{p}^{d ...
Yu Xue, Lou Ben Gong
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Open Mathematics, 2020 A Cayley graph Γ\Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Γ\Gamma (note that the right regular representation of G is always an automorphism group of Γ ...
Pan Jiangmin
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Maximal subgroups of finite groups avoiding the elements of a generating set [PDF]
, 2018 We give an elementary proof of the following remark: if G is a finite group and { g1, \u2026 , gd} is a generating set of G of smallest cardinality, then there exists a maximal subgroup M of G such that M 29 { g1, \u2026 , gd} = 05. This result leads us
Lucchini, Andrea, Spiga, Pablo
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2-closures of primitive permutation groups of holomorph type
Open Mathematics, 2019 The 2-closure G(2) of a permutation group G on a finite set Ω is the largest subgroup of Sym(Ω) which has the same orbits as G in the induced action on Ω × Ω.
Yu Xue, Pan Jiangmin
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A classification of primitive permutation groups with finite stabilizers [PDF]
, 2015 We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.Comment: Accepted in J.
Aschbacher +14 more
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Most primitive groups are full automorphism groups of edge-transitive hypergraphs [PDF]
, 2014 We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,Y^G) = G for a random subset Y of X, tends to 1 as n tends to infinity.
Babai, Laszlo, Cameron, Peter J.
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Wave-Shaped Round Functions and Primitive Groups [PDF]
, 2018 Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key ...
Aragona, Riccardo +4 more
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